By changing the coupling parameter $\alpha$, the $\alpha \text{−}{T}_3$ model lattice varies from honeycomb to dice (or $T_3$) lattice. These lattices are composed of three atomic sites per unit cell, arranged in such a way as to support an additional flat band that touches the conduction and valence bands in the energy spectrum. Slight energetic deviations in the equivalence between their atomic sites result in a band gap opening and the appearance of middle-gap states. Although the sensitivity of these lattices to the breaking equivalence of their atomic sites provides interesting electronic and transport properties, it is unknown how this inequivalence affects the additional intraband states. In this paper, we investigated the appearance of chiral states in $\alpha \text{−}{T}_3$ lattices by applying an asymmetric profile of sublattice symmetry-breaking term as a kink potential. We found one-dimensional interface chiral states morphing as the $\alpha$ parameter is tuned, culminating in a flat band for the dice lattice case. We also demonstrate that the presence of a domain wall (two kink profiles separated by a certain distance), combined with adjustment of the interlattice hopping $\alpha$ parameter, results in two chiral states per valley, which have their dispersion strongly dependent on the $\alpha$ parameter, in addition to the bound states emerging with higher energy-momentum values than the chiral states. Our continuum results are validated with tight-binding results for $\alpha \text{−}{T}_3$ nanoribbons assuming mass-term induced kink and kink-antikink potentials.

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• Flat bands
• Surface states
• Valley degrees of freedom
• 2-dimensional systems
• k dot p method